When a shielding material does not exist between a base station device and a mobile station device that moves at a high speed, an environment for propagation of a radio wave is a so-called Racian fading environment. It is known that, in such a case, a Doppler effect on received signals causes a frequency deviation and largely affects the quality of communication.
As a method for estimating the frequencies of received signals, the following method is known. The method is to calculate a correlation between reference signals received at different times and estimate the amount of a phase rotation in an interval between the times when the reference signals are received or estimate a phase difference. Let sk be a transmitted signal at a time k, let hk be a distortion that occurs in the signal due to a propagation path of the signal, let Δf be a deviation of the frequency of the signal, and let nk be white Gaussian noise. Then, the received signal is given by the following Equation (1),rk=ej2πΔfkhksk+nk,   (1)
where ej2πΔfk denotes the phase rotation.
When a carrier wave is removed, the frequency deviation remains. Thus, the aforementioned phase rotation appears in Equation (1). In this case, a correlation z(k, τ) between the received signal rk at the time k and a received signal rk+τ at a time k+τ is represented by the following Equation (2).
                              z          ⁡                      (                          k              ,              τ                        )                          =                                            r                              k                +                τ                                      ⁢                          r              k              *                                =                                                    ⅇ                                  j2π                  ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                  f                  ⁢                                                                          ⁢                  τ                                            ⁢                              h                                  k                  +                  τ                                            ⁢                              h                k                *                            ⁢                              s                                  k                  +                  τ                                            ⁢                              s                k                *                                      +                                          ⅇ                                  j                  ⁢                                                                          ⁢                  2                  ⁢                  π                  ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                                      f                    ⁡                                          (                                              k                        +                        τ                                            )                                                                                  ⁢                              h                                  k                  +                  τ                                            ⁢                              s                                  k                  +                  τ                                            ⁢                              n                k                *                                      +                                                            n                                      k                    +                    τ                                                  ⁡                                  (                                                            ⅇ                                              j                        ⁢                                                                                                  ⁢                        2                        ⁢                        π                        ⁢                                                                                                  ⁢                        Δ                        ⁢                                                                                                  ⁢                        fk                                                              ⁢                                          h                      k                                        ⁢                                          s                      k                                                        )                                            *                        +                                          n                                  k                  +                  τ                                            ⁢                              n                k                *                                                                        (        2        )            
It is assumed that the propagation path does not change in a time period ti and the transmitted signal sk and a transmitted signal sk+τ are the same. Based on this assumption, the average of correlations z(k, τ) is zero in the second term and later due to a characteristic of the white Gaussian noise. Thus, the following Equation (3) is established.E[z(k,τ)]=ej2πΔfτ  (3)
The frequency deviation Δf can be estimated on the basis of the aforementioned results as indicated by the following Equation (4). Note that if the transmitted signals sk and sk+τ are known, the frequency deviation Δf can be estimated according to a simple modified equation.
                              Δ          ⁢                                          ⁢          f                =                                            arg              ⁡                              (                                  E                  ⁡                                      [                                          z                      ⁡                                              (                                                  k                          ,                          τ                                                )                                                              ]                                                  )                                                    2              ⁢              π              ⁢                                                          ⁢              τ                                =                                    1                              2                ⁢                π                ⁢                                                                  ⁢                τ                                      ⁢                                          tan                                  -                  1                                            ⁡                              [                                                      Im                    ⁡                                          (                                              E                        ⁡                                                  [                                                      z                            ⁡                                                          (                                                              k                                ,                                τ                                                            )                                                                                ]                                                                    )                                                                            Re                    ⁡                                          (                                              E                        ⁡                                                  [                                                      z                            ⁡                                                          (                                                              k                                ,                                τ                                                            )                                                                                ]                                                                    )                                                                      ]                                                                        (        4        )            
“3GPP (Third Generation Partnership Project) contribution, R4-060149, “Discussion on AFC problem under high speed train environment”, NTT DoCoMo, USA, Feb. 13-17, 2006” and “P. Moose, “A Technique for Orthogonal Frequency Division Multiplexing Frequency Offset Correction”, IEEE Trans. Commun., vol. 42, no. 10, October. 1994” are examples of related art.